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          <h2 id="完全背包介绍"><a class="markdownIt-Anchor" href="#完全背包介绍"></a> 完全背包介绍</h2>
<h3 id="1-问题描述"><a class="markdownIt-Anchor" href="#1-问题描述"></a> 1、问题描述</h3>
<p>有N件物品和一个最多能背重量为W的背包。第i件物品的重量是weight[i]，得到的价值是value[i] 。<strong>每件物品都有无限个（也就是可以放入背包多次）</strong>，求解将哪些物品装入背包里物品价值总和最大。</p>
<p><strong>完全背包和01背包问题唯一不同的地方就是，每种物品有无限件</strong>。</p>
<h3 id="2-核心代码"><a class="markdownIt-Anchor" href="#2-核心代码"></a> 2、核心代码</h3>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 先遍历物品，再遍历背包</span></span><br><span class="line"><span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; weight.size(); i++) &#123; <span class="comment">// 遍历物品</span></span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> j = weight[i]; j &lt;= bagWeight ; j++) &#123; <span class="comment">// 遍历背包容量</span></span><br><span class="line">        dp[j] = max(dp[j], dp[j - weight[i]] + value[i]);</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
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          <h2 id="01背包介绍"><a class="markdownIt-Anchor" href="#01背包介绍"></a> 01背包介绍</h2>
<p>有n件物品和一个最多能背重量为w 的背包。第i件物品的重量是weight[i]，得到的价值是value[i] 。<strong>每件物品只能用一次</strong>，求解将哪些物品装入背包里物品价值总和最大。</p>
<p><img src="https://code-thinking-1253855093.file.myqcloud.com/pics/20210117175428387.jpg" alt="动态规划-背包问题"></p>
<h3 id="背包问题整体框图"><a class="markdownIt-Anchor" href="#背包问题整体框图"></a> 背包问题整体框图</h3>
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          <h2 id="题目汇总"><a class="markdownIt-Anchor" href="#题目汇总"></a> 题目汇总</h2>
<table>
<thead>
<tr>
<th>题目</th>
<th>题解</th>
</tr>
</thead>
<tbody>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/fibonacci-number/">509. 斐波那契数</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/climbing-stairs/">70. 爬楼梯</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/min-cost-climbing-stairs/">746. 使用最小花费爬楼梯</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/unique-paths/">62.不同路径</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/unique-paths/solutions/2361753/dong-tai-gui-hua-shi-jian-fu-za-du-on2-b-jh8t/">https://leetcode.cn/problems/unique-paths/solutions/2361753/dong-tai-gui-hua-shi-jian-fu-za-du-on2-b-jh8t/</a></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/integer-break/">343.整数拆分</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/unique-binary-search-trees/">96.不同的二叉搜索树</a></td>
<td></td>
</tr>
<tr>
<td>打家劫舍专题</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/house-robber/">198.打家劫舍</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/house-robber-ii/">213.打家劫舍II</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/house-robber-iii/">337.打家劫舍 III</a>（树型dp）</td>
<td></td>
</tr>
<tr>
<td>买卖股票的最佳时间专题</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/best-time-to-buy-and-sell-stock/">121.买卖股票的最佳时机</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/best-time-to-buy-and-sell-stock-ii/">122.买卖股票的最佳时机II</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/best-time-to-buy-and-sell-stock-iii/">123.买卖股票的最佳时机III</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/best-time-to-buy-and-sell-stock-iv/">188.买卖股票的最佳时机IV</a></td>
<td></td>
</tr>
<tr>
<td>不连续子序列问题</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/longest-increasing-subsequence/">300.最长递增子序列</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/longest-common-subsequence/">1143. 最长公共子序列</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/uncrossed-lines/">1035.不相交的线</a></td>
<td></td>
</tr>
<tr>
<td>连续子序列问题</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/longest-continuous-increasing-subsequence/">674. 最长连续递增序列</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/maximum-length-of-repeated-subarray/">718. 最长重复子数组</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/maximum-subarray/">53. 最大子序和</a></td>
<td></td>
</tr>
<tr>
<td>编辑距离</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/is-subsequence/">392. 判断子序列</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/distinct-subsequences/">115. 不同的子序列</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/delete-operation-for-two-strings/">583. 两个字符串的删除操作</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/edit-distance/">72. 编辑距离</a></td>
<td></td>
</tr>
<tr>
<td>回文问题</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/palindromic-substrings/">647. 回文子串</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/longest-palindromic-subsequence/">516.最长回文子序列</a></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
</tbody>
</table>
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          <h2 id="题目汇总"><a class="markdownIt-Anchor" href="#题目汇总"></a> 题目汇总</h2>
<table>
<thead>
<tr>
<th>题目</th>
<th>题解</th>
</tr>
</thead>
<tbody>
<tr>
<td>组合问题</td>
<td>收集状态树中所有的叶子节点</td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/combinations/">77.组合</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/combinations/solutions/2332183/jian-zhi-you-hua-shi-jian-1ms-by-dpbirde-p6q8/">https://leetcode.cn/problems/combinations/solutions/2332183/jian-zhi-you-hua-shi-jian-1ms-by-dpbirde-p6q8/</a></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/combination-sum-iii/">216.组合总和III</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/combination-sum/">39. 组合总和</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/combination-sum-ii/">40.组合总和II</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/combination-sum-ii/solutions/2337184/hui-su-jian-zhi-qu-zhong-shi-jian-2ms-by-nwjs/">https://leetcode.cn/problems/combination-sum-ii/solutions/2337184/hui-su-jian-zhi-qu-zhong-shi-jian-2ms-by-nwjs/</a></td>
</tr>
<tr>
<td>字符串分割问题</td>
<td>收集状态树中所有的叶子节点</td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/palindrome-partitioning/">131.分割回文串</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/palindrome-partitioning/solutions/2337113/hui-su-fa-fen-ge-zi-fu-chuan-shi-jian-fu-5e10/">https://leetcode.cn/problems/palindrome-partitioning/solutions/2337113/hui-su-fa-fen-ge-zi-fu-chuan-shi-jian-fu-5e10/</a></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/restore-ip-addresses/">93.复原IP地址</a></td>
<td></td>
</tr>
<tr>
<td>子集问题</td>
<td>收集状态树中所有的节点</td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/subsets/">78.子集</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/subsets/solutions/2337153/hui-su-fa-qiu-zi-ji-shi-jian-fu-za-du-o2-nywf/">https://leetcode.cn/problems/subsets/solutions/2337153/hui-su-fa-qiu-zi-ji-shi-jian-fu-za-du-o2-nywf/</a></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/subsets-ii/">90.子集II</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/subsets-ii/solutions/2337192/hui-su-qu-zhong-jie-jue-zi-ji-wen-ti-shi-04p4/">https://leetcode.cn/problems/subsets-ii/solutions/2337192/hui-su-qu-zhong-jie-jue-zi-ji-wen-ti-shi-04p4/</a></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/non-decreasing-subsequences/">491.递增子序列</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/non-decreasing-subsequences/solutions/2337222/hui-su-ha-xi-qu-zhong-jian-zhi-shi-jian-gqwio/">https://leetcode.cn/problems/non-decreasing-subsequences/solutions/2337222/hui-su-ha-xi-qu-zhong-jian-zhi-shi-jian-gqwio/</a></td>
</tr>
<tr>
<td>排列问题</td>
<td>收集状态树中的叶子节点，每次都从问题集中选择一个没有使用过的元素</td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/permutations/">46.全排列</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/permutations/solutions/2340066/hui-su-shi-jian-1ms-by-dpbirder-bbhy/">https://leetcode.cn/problems/permutations/solutions/2340066/hui-su-shi-jian-1ms-by-dpbirder-bbhy/</a></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/permutations-ii/">47.全排列 II</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/permutations-ii/solutions/2340108/hui-su-qu-zhong-shi-jian-1ms-by-dpbirder-9sw4/">https://leetcode.cn/problems/permutations-ii/solutions/2340108/hui-su-qu-zhong-shi-jian-1ms-by-dpbirder-9sw4/</a></td>
</tr>
<tr>
<td>棋盘问题</td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/n-queens/">51.N皇后</a></td>
<td></td>
</tr>
<tr>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/sudoku-solver/">37.解数独</a></td>
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          <h2 id="什么是回溯算法"><a class="markdownIt-Anchor" href="#什么是回溯算法"></a> 什么是回溯算法</h2>
<p>回溯算法是一种通过尝试逐步构建解决方案来递归解决问题的算法，一次一个删除那些在任何时间都无法满足问题约束的解决方案，可以看作是一种高级的暴力算法。</p>
<h2 id="如何理解回溯算法"><a class="markdownIt-Anchor" href="#如何理解回溯算法"></a> 如何理解回溯算法</h2>
<p>回溯算法解决的问题都可以抽象成树形结构，因为回溯算法都是在集合中找子集，集合的大小构成了树的宽度，递归的深度构成了树的深度，递归要终止就要有终止条件，所以必然是一颗高度有限的N叉树。</p>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-tree/">236. 二叉树的最近公共祖先</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-tree/solutions/2303133/hou-xu-bian-li-hui-su-shi-jian-fu-za-du-x54ok/">https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-tree/solutions/2303133/hou-xu-bian-li-hui-su-shi-jian-fu-za-du-x54ok/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-search-tree/">235. 二叉搜索树的最近公共祖先</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-search-tree/solutions/2306710/li-yong-bstde-you-xu-xing-shi-yong-zhong-me9y/">https://leetcode.cn/problems/lowest-common-ancestor-of-a-binary-search-tree/solutions/2306710/li-yong-bstde-you-xu-xing-shi-yong-zhong-me9y/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/insert-into-a-binary-search-tree/">701.二叉搜索树中的插入操作</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/delete-node-in-a-bst/">450.删除二叉搜索树中的节点</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/trim-a-binary-search-tree/">669. 修剪二叉搜索树</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/trim-a-binary-search-tree/solutions/2299625/hou-xu-guo-cheng-si-lu-jian-ji-ming-liao-yhdb/">https://leetcode.cn/problems/trim-a-binary-search-tree/solutions/2299625/hou-xu-guo-cheng-si-lu-jian-ji-ming-liao-yhdb/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/convert-sorted-array-to-binary-search-tree/">108.将有序数组转换为二叉搜索树</a></td>
<td></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/convert-bst-to-greater-tree/">538.把二叉搜索树转换为累加树</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/convert-bst-to-greater-tree/solutions/2300969/you-zhong-zuo-bian-li-lei-zhong-xu-bian-d969n/">https://leetcode.cn/problems/convert-bst-to-greater-tree/solutions/2300969/you-zhong-zuo-bian-li-lei-zhong-xu-bian-d969n/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/search-in-a-binary-search-tree/">700.二叉搜索树中的搜索</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/search-in-a-binary-search-tree/solutions/2295076/di-gui-die-dai-cha-zhao-bstde-zhi-shi-ji-mz2m/">https://leetcode.cn/problems/search-in-a-binary-search-tree/solutions/2295076/di-gui-die-dai-cha-zhao-bstde-zhi-shi-ji-mz2m/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/validate-binary-search-tree/">98.验证二叉搜索树</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/validate-binary-search-tree/solutions/2295125/si-chong-fang-fa-yan-zheng-bstshu-shi-ji-mycw/">https://leetcode.cn/problems/validate-binary-search-tree/solutions/2295125/si-chong-fang-fa-yan-zheng-bstshu-shi-ji-mycw/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/minimum-absolute-difference-in-bst/">530.二叉搜索树的最小绝对差</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/minimum-absolute-difference-in-bst/solutions/2295161/li-yong-bstde-you-xu-xing-jie-jue-wen-ti-29jl/">https://leetcode.cn/problems/minimum-absolute-difference-in-bst/solutions/2295161/li-yong-bstde-you-xu-xing-jie-jue-wen-ti-29jl/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/find-mode-in-binary-search-tree/">501.二叉搜索树中的众数</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/find-mode-in-binary-search-tree/solutions/2298603/li-yong-bstyou-xu-xing-yi-ci-bian-li-cha-o0ox/">https://leetcode.cn/problems/find-mode-in-binary-search-tree/solutions/2298603/li-yong-bstyou-xu-xing-yi-ci-bian-li-cha-o0ox/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/symmetric-tree/">101. 对称二叉树</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/symmetric-tree/solutions/2291747/san-chong-fang-fa-jie-jue-shi-jian-fu-za-0xas/">https://leetcode.cn/problems/symmetric-tree/solutions/2291747/san-chong-fang-fa-jie-jue-shi-jian-fu-za-0xas/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/maximum-depth-of-binary-tree/">104.二叉树的最大深度</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/maximum-depth-of-binary-tree/solutions/2292856/san-chong-fang-fa-qiu-zui-da-shen-du-shi-9dw9/">https://leetcode.cn/problems/maximum-depth-of-binary-tree/solutions/2292856/san-chong-fang-fa-qiu-zui-da-shen-du-shi-9dw9/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/minimum-depth-of-binary-tree/">111.二叉树的最小深度</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/minimum-depth-of-binary-tree/solutions/2313324/qian-xu-hou-xu-die-dai-san-chong-fang-fa-e5gg/">https://leetcode.cn/problems/minimum-depth-of-binary-tree/solutions/2313324/qian-xu-hou-xu-die-dai-san-chong-fang-fa-e5gg/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/count-complete-tree-nodes/">222.完全二叉树的节点个数</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/count-complete-tree-nodes/solutions/2313340/li-yong-wan-quan-er-cha-shu-de-xing-zhi-qd5q2/">https://leetcode.cn/problems/count-complete-tree-nodes/solutions/2313340/li-yong-wan-quan-er-cha-shu-de-xing-zhi-qd5q2/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/balanced-binary-tree/">110.平衡二叉树</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/balanced-binary-tree/solutions/2313351/hou-xu-bian-li-ji-suan-shu-de-shen-du-sh-f18p/">https://leetcode.cn/problems/balanced-binary-tree/solutions/2313351/hou-xu-bian-li-ji-suan-shu-de-shen-du-sh-f18p/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/binary-tree-paths/">257.二叉树的所有路径</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/binary-tree-paths/solutions/2329292/qian-xu-bian-li-shi-jian-1ms-by-dpbirder-5h9z/">https://leetcode.cn/problems/binary-tree-paths/solutions/2329292/qian-xu-bian-li-shi-jian-1ms-by-dpbirder-5h9z/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/sum-of-left-leaves/">404.左叶子之和</a></td>
<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/sum-of-left-leaves/solutions/2313383/li-yong-fu-jie-dian-pan-duan-shi-fou-wei-fu0t/">https://leetcode.cn/problems/sum-of-left-leaves/solutions/2313383/li-yong-fu-jie-dian-pan-duan-shi-fou-wei-fu0t/</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/find-bottom-left-tree-value/">513.找树左下角的值</a></td>
<td></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/path-sum/">112.路径总和</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/path-sum-ii/">113.路径总和II</a></td>
<td></td>
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<td>二叉树的修改与改造</td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/invert-binary-tree/">226.翻转二叉树</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/construct-binary-tree-from-inorder-and-postorder-traversal/">106.从中序与后序遍历序列构造二叉树</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/binary-tree-preorder-traversal/">144.二叉树的前序遍历</a></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/binary-tree-inorder-traversal/">94.二叉树的中序遍历</a></td>
<td></td>
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<td><a target="_blank" rel="noopener" href="https://leetcode.cn/problems/binary-tree-postorder-traversal/">145.二叉树的后序遍历</a></td>
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